How can I give a wet effect to my character mouth and eyelids
If you're using the default Blender Renderer try making the surface smoothly bumpy so there are plenty of angles to catch the light, and turn up Hardness to make the specular highlights sharper.  You could use extra lights at angles to the camera, placed here and there, with Diffuse unticked so it only gives Specular light, and if those extra lights interfere with your general lighting, you can put the lights on their own layer and tick This Layer Only, then put the gum on that layer too.  You can have more than one layer open by pressing Shift while clicking on the layers.  (You move an object to another layer with the M key, with object selected.)